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Zbl 1203.54037
Property P in G-metric spaces.
(English)
[J] Fixed Point Theory Appl. 2010, Article ID 401684, 12 p. (2010). ISSN 1687-1812/e

The authors establish two fixed point theorems for some contractive-type maps on complete $G$-metric spaces. It is also shown that if $(X,G)$ is a complete $G$-metric space and $T$ is a self-map of $X$ satisfying the hypotheses of any of the two theorems then the maps $F^n$ have the same fixed point set, for all $n\in \Bbb{N}$.
MSC 2000:
*54H25 Fixed-point theorems in topological spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: $G$-metric space; fixed point; property $P$

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